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The Uncertainty Quantification Toolbox

The Uncertainty Quantification Toolbox (UQTools) is a software package designed to efficiently quantify the impact of parametric uncertainty on engineering systems. UQTools was designed to be discipline independent, employing very generic representations of the system models and uncertainty. Specifically, UQTools accepts linear and nonlinear system models and permits arbitrary functional dependencies between the system’s measures of interest and the probabilistic or non-probabilistic parametric uncertainty.

There are many novel features built into UQTools, but the primary innovation is related to the development of set bounding techniques and their application to reliability analysis. Set bounding techniques will be referred to as homothetic deformations in later sections of the document. In contrast to conventional approaches to uncertainty quantification, these techniques do not require the upfront definition of probabilistic models for the uncertain parameters. Instead, UQTools generates tight bounding sets to regions in the parameter space of acceptable system performance (safe domain) or unacceptable system performance (failure domain). These bounding sets are constructed using simple geometries (hyper-spheres or hyper-rectangles). Once these bounding sets have been calculated, the reliability analysis corresponding to particular probabilistic uncertainty models can be efficiently carried out. This feature enables accommodating for changes in uncertainty models with little additional computational effort. Figures of merit for uncertainty quantification that result from these techniques are robustness metrics that measure the separation between any given parameter realization and the failure domain, upper bounds to the failure probability and accurate estimates to failure probability.

The UQTools software package is available free of charge to qualified US citizens. Please click here to request UQTools.